Properties

Label 48.2.c
Level 48
Weight 2
Character orbit c
Rep. character \(\chi_{48}(47,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 16
Trace bound 0

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Defining parameters

Level: \( N \) = \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 48.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(48, [\chi])\).

Total New Old
Modular forms 14 2 12
Cusp forms 2 2 0
Eisenstein series 12 0 12

Trace form

\( 2q - 6q^{9} + O(q^{10}) \) \( 2q - 6q^{9} - 4q^{13} + 12q^{21} + 10q^{25} - 20q^{37} - 10q^{49} - 12q^{57} + 28q^{61} + 20q^{73} + 18q^{81} - 36q^{93} - 28q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(48, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
48.2.c.a \(2\) \(0.383\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{3}+2\zeta_{6}q^{7}-3q^{9}-2q^{13}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( \)
$3$ \( 1 + 3 T^{2} \)
$5$ \( ( 1 - 5 T^{2} )^{2} \)
$7$ \( ( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} ) \)
$11$ \( ( 1 + 11 T^{2} )^{2} \)
$13$ \( ( 1 + 2 T + 13 T^{2} )^{2} \)
$17$ \( ( 1 - 17 T^{2} )^{2} \)
$19$ \( ( 1 - 8 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \)
$23$ \( ( 1 + 23 T^{2} )^{2} \)
$29$ \( ( 1 - 29 T^{2} )^{2} \)
$31$ \( ( 1 - 4 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \)
$37$ \( ( 1 + 10 T + 37 T^{2} )^{2} \)
$41$ \( ( 1 - 41 T^{2} )^{2} \)
$43$ \( ( 1 - 8 T + 43 T^{2} )( 1 + 8 T + 43 T^{2} ) \)
$47$ \( ( 1 + 47 T^{2} )^{2} \)
$53$ \( ( 1 - 53 T^{2} )^{2} \)
$59$ \( ( 1 + 59 T^{2} )^{2} \)
$61$ \( ( 1 - 14 T + 61 T^{2} )^{2} \)
$67$ \( ( 1 - 16 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} ) \)
$71$ \( ( 1 + 71 T^{2} )^{2} \)
$73$ \( ( 1 - 10 T + 73 T^{2} )^{2} \)
$79$ \( ( 1 - 4 T + 79 T^{2} )( 1 + 4 T + 79 T^{2} ) \)
$83$ \( ( 1 + 83 T^{2} )^{2} \)
$89$ \( ( 1 - 89 T^{2} )^{2} \)
$97$ \( ( 1 + 14 T + 97 T^{2} )^{2} \)
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